Triangle calculator
Give three sides and get every angle, the area, the perimeter and the type.
- Runs in your browser — nothing you enter is uploaded
- No sign-up, no quotas, free to use as often as you like
How it works
Three side lengths determine a triangle completely — every angle, the area, everything. Getting there by hand means the cosine rule three times and Heron's formula, which is a lot of arithmetic to do without a slip.
It checks the triangle can exist first
Any two sides must add up to more than the third. Lengths of 1, 2 and 10 describe nothing, and a calculator that returns an angle for them is producing nonsense. This reports the problem instead.
How the angles are found
The cosine rule, applied to each angle in turn. As a check, the three angles are added up and shown — they should come to 180 degrees, and seeing that confirms the calculation held together.
Area without the height
Heron's formula gives the area from the three sides alone, with no need to know a height. The height to side a is then derived from the area, which is usually easier than measuring it.
Type, and the circles
Whether the triangle is acute, right-angled or obtuse, and whether it is equilateral, isosceles or scalene. The circumradius (the circle through all three corners) and inradius (the largest circle that fits inside) are given too, since they are awkward to derive and frequently asked for.
Triangle calculator — questions
Why does it say my triangle is impossible?
Because two of the sides do not add up to more than the third, which means no such triangle exists.
Can I enter angles instead of sides?
Not in this version — it solves from three sides, which is the case that determines the triangle completely.
How is the area calculated?
By Heron's formula, which needs only the three side lengths.
What are circumradius and inradius?
The radius of the circle through all three vertices, and of the largest circle that fits inside.
How does it know if it is right-angled?
By comparing the square of the longest side with the sum of the squares of the other two.